It is known that divers using air breathing equipment run the risk of nitrogen embolism when ascending to the surface after a dive. To avoid this risk a diver should effect his ascent in stages with one or more decompression halts at specific depths. The depths at which these decompression halts should be made and the necessary dwell times at these depths are set out in decompression tables as a function of the maximum depth reached during the dive and the length of time at this maximum depth. The use of decompression tables is rather inconvenient and complicated when the dive is performed at a variable depth and when repeated dives are performed separated in time.
Due to these difficulties, devices called decompression meters have become widely used, these devices being designed to automatically present to the diver the data necessary for him to effect an ascent without incurring the risk of embolism.
There exist various forms of decompression meter all of which have a structure substantially as set out at the beginning of the present specification. These decompression meters can be classified into two main groups; namely those with a linear scale and those with a circular scale.
In the following introductory discussion of decompression meters those having a linear-scale will be primarily considered, it being understood that the discussion is valid, mutatis mutandis, for meters with a circular scale.
The introductory discussion will be made with reference to FIGS. 1 to 5 of the accompanying drawings, in which:
FIG. 1 is a diagrammatic representation of the linear scale and movable index of a standard decompression meter;
FIG. 2 is an experimentally-determined table for a known type of decompression meter of the FIG. 1 form, the table giving values for the displacement of the movable index of the meter as a function of the maximum depth reached during a dive and of the dwell time at this depth;
FIG. 3 is an experimentally-determined decompression diagram for the same decompression meter as used in the preparation of FIG. 2, the diagram indicating the relationship between the displacement of the index and the return times of the index towards the scale origin in a simulated ascent test,
FIG. 4 is a table, obtained by calculation, of the errors in decompression time presented by the decompression meter used in the preparation of FIGS. 2 and 3, the errors being tabulated as a function of the maximum depth of dive and of the dwell time at that depth; and
FIG. 5 is a table of guide numbers for the correction of the errors in decompression time presented by the meter as a function of the maximum depth reached and of the dwell time at this depth.
As shown in FIG. 1, the linear scale of a standard decompression meter is subdivided into two successive sections, respectively indicated by A and B.
The first section A extends from the origin of the scale and consists of a strip which, conventionally, is coloured blue. The second section B, which follows on immediately from the first, is constituted by a strip of greater height than that used for the scale section A. The strip used for section B is conventionally coloured red and is subdivided into successive zones, each of which indicates the depth at which a decompression halt should be made during ascent from a dive. In FIG. 1, these depths are indicated in meters (3-3-3-6-9-12-15-18).
An index I is movable along the scale, the displacement of the index from the scale origin being represented by S.
During a dive, the index I is caused to move from the scale origin towards the right. If, at the beginning of the ascent from the dive, the index I has not reached the scale section B this means that the diver does not have to effect any decompression halts during the ascent.
If, on the other hand, the index I is in the scale section B at the beginning of the ascent, this means that the diver must effect one or more decompression halts. During the ascent, the index returns back slowly across the scale from the right to the left as viewed in FIG. 1. The diver must remain at the depth indicated by the index I on the scale section B until the index has moved back to a shallower depth whereupon the diver can ascend to this latter depth. Thus, in the the situation illustrated in FIG. 1, in which the index I is located in correspondence to the zone marked 9, the diver must remain at the depth of nine meters for the whole of the time taken by the index to reach the left hand end of the zone "9". Thereafter, the diver will have to halt at 6 meters for the whole of the time taken by the index I to traverse the zone marked "6" from right to left and so on.
To adapt the actual operation of the decompression meter to the data provided by the decompression tables most in use, the scale carries various corrections. The correction actually used is based on the duration of the dive at the maximum depth. This duration is usually called "Bottom Time" or "B.T.". For this purpose the zone representing the decompression halt at 3 meters is divided into three parts each with a corresponding range of B.T. These three parts of zone "3" are given a stepped outline to facilitate their identification by the diver.
As indicated in FIG. 1, if the B.T. has been from 0 to 30 minutes, the diver when ascending need only halt at 3 meters for the time taken by the index I to traverse the first, right hand, part of zone "3" from right to left. For a B.T. lying between 30 minutes and 1 hour, the diver must remain at 3 meters until the index I has reached the left hand end of the middle part of zone "3". Finally, for a B.T. from 1 h. to 2 h., the diver must remain at 3 meters for the whole of the time taken for the index I to completely traverse the three parts of zone "3".
Notwithstanding the foregoing expedient for correcting the decompression time indicated by the meter, substantial errors are still present in the indicated decompression times as compared with the times set out in the standard decompression tables.
Summarised below are the results of a study carried out on the deficiencies of the standard form of decompression meter scale, the object of this study being to devise a different form of scale less subject to error and generally safer. For this purpose a large amount of data was collected on the operation of standard decompression meters; this data was then studied by a graphic method as this permits the behaviour of a linear scale decompression meter to be analysed with considerable precision.
The study was carried out on a standard linear scale decompression meter of a widely used and well known type, commercially available under the designation "DCS" and produced by SOS s.a.s. of Turin (Italy).
The "DCS" decompression meter was subjected to a constant pressure for different exposure times (corresponding to different "B.T.s") and for each of these times the corresponding value of the displacement S (in millimeters) of the index I was recorded. The test was repeated for different values of constant pressure to obtain a so-called pressure diagram (not illustrated), from which the Table shown in FIG. 2 was derived, for greater ease of use. In this Table, the pressure values have been replaced by the corresponding depth of water H in feet (1 foot equals 0.3048 meters), and the values of the displacement S (in millimeters) have been recorded as a function of the depth H and of the B.T. (in minutes).
The purpose of the Table of FIG. 2 will become clear hereinafter.
A decompression diagram (FIG. 3) was also obtained for the "DCS" decompression meter. This diagram shows the relationship between the displacements of the index I from the scale origin (in millimeters) and the time T (in minutes) during decompression. The diagram of FIG. 3 was obtained very simply by saturating the decompression meter, (that is, by causing the index I to be displaced to the end of the scale) and then allowing the index to return (towards the left in FIG. 1) against a controlled opposing pressure which is successively reduced in correspondence to the decompression halts made at various depths of water. Examination of the diagram of FIG. 3 reveals that in the region in which the decompression halts (left part of the diagram), are found, the curve is not exponential, but practically a straight line the equation of which is as follows: EQU T=K.sub.1 (S-GN') (1)
where:
Although the tests were performed with a particular kind of instrument, those skilled in the art can easily verify that equation (1) is valid for all types of decompression meters (both linear scale and circular scale types) having the general structure as mentioned at the beginning. All that varies from one type of decompression meter to another is the value of K.sub.1. Moreover, in a circular scale decompression meter the values of S and GN' can be expressed in length of arc or in degrees. In the particular type of "DCS" meter tested, and with S and GN' expressed in millimeters, one has: EQU K.sub.1 =3.4 (min/mm)
In FIG. 1 there are indicated in millimeters the values of GN' corresponding to the three different B.T.s discussed above for the said "DCS" instrument.
Now supposing a dive to 90 feet (27.4 meters) and of a B.T. duration=70 minutes is simulated with the "DCS" meter under consideration. The U.S. Navy decompression tables--revised edition of 1958--neglecting the descent and ascent times between one decompression height and another, provide the following data:
From the Table of the values of S for the "DCS" meter (FIG. 2) one finds that S=60 mm.
Now, for B.T.=70 minutes it is recommended that the first scale step be used to determine the length of the decompression halt at 3 meters, the corresponding value of GN' being 41.8 millimeters. The total decompression time T.sub.dec as determined by the decompression meter will thus be: EQU T.sub.dec =3.4(S-GN')=3.4(60-41.8)=61.8 min.
Therefore, there will be an error, with respect to the U.S. Navy tables, equal to: EQU T.sub.dec -T.sub.tab =61.8-37=+24.8 min.
It will be appreciated that this error can be considered as originating from the incorrect choice of the value of GN' for the particular decompression starting conditions concerned.
By performing the above calculation for all the values provided by the U.S. Navy tables it is possible to compile a table of the errors in the decompression meter. Such a table is shown in FIG. 4 and in this table the vertical lines mark the boundary between the area where no decompression halts are required (the marking of these lines being in accordance with the U.S. Navy tables). The framed numbers represent the time in minutes by which the meter provides an under-estimate of the decompression time indicated as necessary by the U.S. Navy tables, whilst the non framed numbers represent the overestimate of the necessary decompression time by the meter.
From an examination of the table of FIG. 4 it is apparent that the decompression meter is safe in depths up to 30 meters; at depths less than 30 meters it indicates the necessity for decompression too soon and provides exaggerated values for the necessary decompression time. Although this erroneous indication by the meter is safe, it results in the diver going through unnessary or over-long decompressions, with a large wastage of air, in the range of depths most frequently used.
At depths greater than 30 meters the decompression meter will be late in indicating the need for decompression halts and, when finally it does indicate the need for such halts, the decompression times indicated are too high. The delay in indicating the need for decompression halts is on average from 5 to 10 minutes which represents a real risk for the diver who might as a consequence suffer from the phenomenon of embolism.
By re-arranging equation (1), the following relationship is derived: EQU GN'=S-(T/3.4)
From this relation and using the data provided from the U.S. Navy tables, it is possible to derive the value of GN' required for each set of decompression starting conditions in order to have a decompression meter with nil error.
It will be appreciated that the three values of GN' provided on the FIG. 1 meter and appropriate for different decompression starting conditions, are an attempt to provide a variation in the value of GN' in order to minimise the meter error. As will be shown hereinafter, the stated desiderata for choosing a particular one of the three available values of GN' are far from ideal.
At this stage it is convenient to introduce a number GN (to be known as the "guide number") which is related to GN' by the following relationship: EQU GN=GN'-K.sub.2
In the case of the "DCS" linear scale decompression meter investigated, it is seen that the GN' corresponding to a B.T. lying between 1 h and 2 h is 41.8 millimeters. It is a matter of an arbitary value, but the order of magnitude of which is convenient for the particular type of instrument considered.
For this type of meter a value of K.sub.2 =37 will be chosen. In practice this can be treated as equivalent to a displacement of the scale origin of 37 millimeters towards the right as viewed in FIG. 1 with the new value of GN' then being called GN. The reasons for choosing K.sub.2 =37 will become clear below. For the moment it is sufficient to note that a displacement of the origin of the scale towards the right, but within the first scale section A (the "blue" zone) does not introduce any complications, since when the index I has passed the second scale section B (the "red zone") on its return towards the left, it is no longer necessary to perform decompression halts.
An examplary calculation of the guide number GN will now be made: putting H=60 feet=18.3 meters and B.T.=100', from the U.S. Navy tables a total decompression time T.sub.tab =14' is obtained. From the FIG. 2 table, the value of S' for the meter is given as 54.5 millimeters.
By substituting these values into the preceding relationships it is possible to calculate the value of GN' which would give the correct decompression time: EQU GN'=S-(T.sub.tab /3.4)=54.5-(14/3.4)=50.38 mm.
The corresponding value of GN is then: EQU GN=50.38-37=13.38.perspectiveto.13.
By carrying out similar calculations for all the values given in the U.S. Navy tables, a table of guide numbers GN can be built up (see FIG. 5) giving, for different decompression starting conditions, the guide number corresponding to the correct indication of decompression time by the meter.
In the FIG. 5 table, the vertical thick lines furthest to the left marks the boundary of the area of the table corresponding to the need for decompression halts as indicated by the U.S. Navy tables; the single stepped line indicates the operational bounds for a diver provided with cylinder breathing apparatus of 4000 liters; the double stepped line indicates the operational bounds for a diver provided with a double-cylinder breathing apparatus having a capacity of 8000 liters.
The adjustment to the value of GN' (and thus GN) used with the fixed scales of known decompression meters, such as the linear decompression meter previously considered, is effected on the basis only of the "Bottom Time" (B.T.). Thus, for a scale such as that of FIG. 1, one has:
These values of GN have been marked in on the table of FIG. 5 over the corresponding ranges of the B.T. scale.
As can be seen from the table, the values of GN used by the meter bear little relationship to the values required to give the correct decompression times. Indeed, it could be said that the chosen values of GN have the opposite effect from what is required. Thus for example, where a standard decompression meter uses a value of GN=5, the table indicates that the optimum GN for the same B.T. range is of the order of 12. In the other two B.T. ranges, the correspondence between the GN of the standard decompression meter and the optimum GN is also poor.
If, instead, the FIG. 5 table is subdivided into three depth bands in the manner indicated on the right of the figure, it is seen that a mean GN equal to 12 is appropriate for the depth band which goes from 15 to 27 meters; a mean GN equal to 9 is appropriate to the depth band H which goes from 30 to 36 meters, and a mean GN equal to 5 is appropriate to the depth band H of 40 meters and more. With this subdivision on the basis of the depth H rather than on the basis of the B.T., the errors in decompression time as determined by the meter are practically nil down to a depth of 30 meters. From 30 meters to 60 meters the start of the need for decompression is correctly indicated and any errors in decompression time are on the safe side.
The subdivision of the FIG. 5 table into bands according to maximum depth reached is therefore much more in keeping with what is required than a subdivision on the basis of dwell times at the maximum depth. The only disadvantage of employing the described subdivision according to depth, with for a standard fixed-scale decompression meter, is that for the lower depth ranges, adequate account is not taken of the deeper decompression halts; as a result in the horizontal depth band in which the mean GN is equal to 5, there appear in the table values of GN equal to 15.